Multiplying Polynomials I

Multiplying Polynomials ILearning how to multiply a binomial with a monomial

Rules of Exponents - Review

Before we begin multiplying polynomials let’s review Rules of Exponents

The Invisible Exponent

When an expression does not have a visible exponent its exponent is understood to be 1.

1xx

Product of like bases

When multiplying two expressions with the same base you add their exponents.

For example

mn bb mnb

42 xx 42x6x

Power to a Power

When raising a power to a power you multiply the exponents

For example

mnb )( mnb

42 )(x 42x 8x

Product to a Power

When you have a product of two or more numbers, you raise each factor to the power

For example

mab)( mmba4)4( x 44 *4 x 4256x

Quotient with like bases

When dividing two expressions with the same base, you subtract the exponents

For example

nmm

na

a

a

5

3x

x35x 2x

Negative Powers

When you have negative exponents, flip the term to the other side (top/bottom) of the fraction

Examples

2x 2

1

z2

1

x2z

Zero Power Rule

Anything to the zero power (except 0) is 1

0p 1 025 1 0000,000,1 1303 yxz ))(1)(( 33 yz 33yz

zab

zba4

249

zba 08 za8

Classifying Polynomials

POLYNOMIALS

MONOMIALS

(1 TERM)

BINOMIALS

(2 TERMS)

TRINOMIALS

(3 TERMS)

x2 + 4xx2 x2 + 4x - 4

The Distributive Property - Back with a Vengeance

We will be applying the Distributive Property to multiply polynomials

You will learn the box method for distribution

Distributive Property (Box Method)

-7(5x + 8)

= -35x – 56

Ex. 1

5x + 8

-7 -35x -56

x(x + 4)

= x2 + 4x

Ex. 2

x + 4

x x2 4x

Distributive Property (Box Method)

2x(x - 6)

= 2x2 – 12x

Ex. 3

x - 6

2x 2x2 -12x

3h2(5h - 9)

= 15h3 – 27h2

Ex. 4

5h - 9

3h2 15h3 -27h2

Distributive Property (Box Method)

9p3(2p5 + 6p)

= 18p8 + 54p4

Ex. 5

2p5 +6p

9p3 18p8 +54p4

7k(k9 – 6k)

= 7k10 – 42k2

Ex. 6

k9 - 6k

7k 7k10 -42k2

Questions